star maths assessment indicators

STAR Maths Assessment Indicators

Copyright © 2018 by Southwark Council

Year 1 Emerging Developing Securing

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Count to at least 20, forwards and backwards

Count forwards in twos from 0 to 20 in practical activities

Read and write numbers in numerals to at least 20

Given a number between 1 and 20, identify one more and one less

Order numbers to 20

Identify and represent numbers to 20 using objects, structured apparatus and number tracks

Use the language of more than, less than when comparing numbers/sets of objects to 20

Use ordinal numbers such as first, second and third

Count to at least 50, forwards and backwards, in ones, beginning with 0 or 1 or from any given number

Count forwards and backwards in twos to 20

Count forwards and backwards in tens from 0 to 100

Read and write numbers in numerals to 50

Read and write numbers in words to 10 and match to the numerals


Identify and represent numbers to at least 50 using objects, structured apparatus and number lines/tracks

Recognise place value in teen numbers using practical apparatus

Use the language of equal to, more than, less than (fewer) when comparing numbers/sets of objects to 50

Use ordinal numbers up to ‘tenth’

Count to and across 100, forwards and backwards, in ones, beginning with 0 or 1 or from any given number

Count forwards and backwards in twos, fives and tens from 0 (to the 10th multiple)

Read and write numbers in numerals to 100

Read and write numbers in words to 20 and match to the numerals


Identify and represent numbers within 100 using objects, structured apparatus and number lines

Begin to recognise place value in two digit numbers beyond 20 using practical apparatus

Use the language of equal to, more than, less than (fewer), most, least when comparing numbers/sets of objects to 100

Begin to reason about numbers e.g. What is wrong with this sequence of numbers? 10, 11, 12, 13, 15, 16. How do you know?

Reason about numbers e.g. If Sam puts these numbers in order starting with the smallest, which one would come third? 21, 12, 8, 28, 18. How do you know?

Reason about numbers e.g. What is wrong with this

sequence of numbers?

30, 29, 27, 26, 25. How do you know?

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Recognise and begin to use addition (+), subtraction (-) and equals (=) signs

Add by combining two groups of objects within 10

Subtract by taking away using objects within 10

Using apparatus represent and use number bonds and related subtraction facts to 10

Use addition (+), subtraction (-) and equals (=) signs to record work

Add two one-digit numbers, including 0, crossing the tens boundary, using apparatus e.g. a number track to count on

Subtract a one-digit number, including 0, from a one-digit number or a teens number using apparatus, e.g. a number track to count back

Recall some number bonds and related subtraction facts to 10

Read, write and interpret addition (+), subtraction (-) and equals (=) signs to record work

Recall and use number bonds and related subtraction facts to 10

Add one-digit and two-digit numbers to at least 20, including zero, using apparatus, e.g. a number track/line

Subtract one-digit and two-digit numbers to at least 20, including zero, using apparatus, e.g. a number track/line

Represent and use number bonds and related subtraction facts with numbers to 20

Solve simple problems that involve addition

and subtraction, using concrete objects, with numbers to 10

Solve simple problems that involve addition and subtraction with numbers to at least 10

Solve missing number problems with numbers to at least 10

Solve one-step problems that involve addition with numbers to at least 20

Solve one-step problems that involve subtraction with numbers to at least 20

Solve missing number problems with numbers to at least 20

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Count repeated groups of two in practical contexts

Find doubles of sets of objects, in practical contexts, up to double 5

Find halves of sets of objects, in practical contexts, up to half of 10

Share sets of objects, in practical contexts, up to 10

Count repeated groups of two and ten in practical contexts

Use doubling facts for numbers up to double 6

Use halving facts for numbers up to half of 12

Share and group sets of objects, in practical contexts, to at least 12

Begin to use arrays to support grouping and sharing

Group small quantities, up to 20, in groups of two, five and ten, including using arrays

Use doubling facts for numbers up to double 10

Use halving facts for numbers up to half of 20

Begin to recognise odd and even numbers up to 20

Solve simple problems involving doubling and halving using concrete objects up to 10

Solve simple problems involving sharing using concrete objects, to 10

Solve simple problems involving doubling and halving using concrete objects and pictorial representations to at least 12

Solve simple problems involving grouping and sharing using concrete objects and pictorial representations to at least 12

Solve one-step problems, using the above, by

calculating the answer by using concrete objects,

pictorial representations and arrays to at least 20

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Recognise a half as one of two equal parts of an object or shape

Find half of a number/set of objects with numbers to 10 using practical resources

Recognise, find and name a half (but not using fraction notation) as one of two equal parts of an object or shape



Recognise, find and name a quarter (but not using fraction notation) as one of four equal parts of an objects or shape

Find a quarter of a number/set of objects with numbers to 20 using practical resources

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Compare and describe using direct comparison and comparative language: lengths and heights

Begin to tell the time to the hour using an analogue clock

Know the days of the week

Use simple sequences of events and begin to use appropriate language such as before and after

Recognise and know the value of coins to 10p

Compare and describe using direct comparison and comparative language: mass/weight and capacity

Compare, describe and measure using non-standard units: lengths and heights, mass/weight and capacity

Tell the time to the hour using an analogue clock

Recognise and know the days of the week and months of the year

Sequence the events of a day in chronological order using appropriate language such as before, after, next, morning, afternoon, today, tomorrow and yesterday.

Recognise and know the value of different denominations of coins to 50p

Measure and begin to use simple standard units: length and height (m and cm), mass/weight (kg), capacity (l) and time (hours, minutes and seconds)

Tell the time to the hour and the half past the hour using an analogue clock

Recognise and use language relating to dates, including days of the week, months of the year

Know that there are seven days in a week; 12 months in a year

Recognise and know the value of different denominations of coins to £1; begin to recognise and know the value of £5 and £10 notes




Solve simple measurement problems in a practical context using direct comparison

Solve simple problems in the context of money to 10p

Solve simple measurement problems in a practical context using non-standard units

Solve practical problems involving time

Solve simple problems (including word problems) in the context of money to at least 10p

Solve simple measurement problems in a practical context using non-standard and standard units

Solve simple problems involving the passage of time (one hour later/one hour before)

Solve simple problems (including word problems) in the context of money to 20p

Solve simple problems involving finding different combinations of coins that equal the same amounts of money (within 10p)

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Recognise and name common 2-D shapes such as circle, triangle, square and rectangle

Recognise and name common 3-D shapes such as cubes, cylinders and cones

Recognise simple repeating patterns with shapes

Recognise and name common 2-D shapes in different orientations and sizes such as circle, triangle, square and rectangle

Recognise and name common 3-D shapes such as cuboid, cube, pyramid, sphere, cone and cylinder

Recognise and create simple repeating patterns with shapes

Recognise, name and sort common 2-D shapes (including shapes in different orientations and sizes); begin to describe their properties

Recognise, name and sort common 3-D shapes (including shapes of different sizes); begin to describe their properties

Recognise and create repeating patterns with shapes

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Use the language of position such as top, bottom, on top of, above, below

Respond to and use terms such as first, second, third…

Use the language of position, direction and movement, such as forwards/ backwards

Respond to and use terms such as first, second, third…tenth

Make whole and half turns in practical contexts

Use the language of position, direction and movement, such as forwards, backwards, left, right and between in practical contexts

Describe position, direction and movement, including whole, half and quarter turns (and begin three quarter turns) in practical contexts

Deepening Understanding

Solve more complex problems

Begin to work systematically

Begin to reason mathematically e.g. responds to ‘How do you know?’ questions

Communicate using appropriate mathematical language

Make links between areas of learning

Demonstrate a ‘natural sense of number’




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Count to and across 100, forwards and backwards, in ones, beginning with 0 or 1 or from any given number with confidence

*Count forwards and backwards in steps

of 2, 5 and 10 to the 12th multiple

*Read and write numbers in numerals to 100

Read and write numbers in words beyond 20 and match to the numerals

Given a number, begin to identify ten more and ten less within 100 using structured apparatus (such as a 100 square) and number lines

Order and compare numbers from 0 to 100

*Partition a two-digit number into tens and ones to demonstrate an understanding of place value, using structured resources

Count forwards and backwards in steps of 2, 5 and 10 to the 12

th multiple and begin to count in

steps of 3

Read and write numbers within 100 in numerals and words

Identify the number that is ten more or less within 100

Begin to count on in tens from any one-digit or two-digit number

Position numbers on a number line; **read

numbers on a number line where the scales are in divisions of ones, twos, fives and tens

Order and compare numbers from 0 to 100; begin to use <, > and = signs

Recognise the place value of each digit in a two-digit number, including with the use of practical resources

**Partition any two-digit number into different

combinations of tens and ones, explaining their thinking verbally, in pictures or using structured apparatus

Count in steps of 2, 3, 5 and in tens from 0 forwards and backwards to the 12

th multiple

Counts on in tens from any one-digit or two-digit number to at least 100

Read and write numbers to at least 100 in numerals and words

Position numbers on a number line; ***read numbers

on a number line where the scales are in divisions of ones, twos, fives and tens and where not all the numbers are given, estimating points in between

Identify the number that is ten more or less within 100, and beyond

Order and compare numbers from 0 to 100; use <, > and = signs

Recognise the place value of each digit in a two-digit number, with confidence

*Solve number and practical problems

that involve counting in twos, fives and tens from 0 e.g. count a set of 5p coins in a purse

Reason about numbers and place value e.g. what number is missing from this sequence? 8,10,14,16, 18. How do you know?

Solve number and practical problems that involve the above

Reason about number and place value e.g. 55, 25, 52, 15, 50. If you put these numbers in order, starting with the smallest, which one would come third? How did you order these numbers?

Solve number, practical and word problems that involve the above

Reason about number and place value e.g. what is wrong with this sequence of numbers? 35, 30, 25, 15, 10. How do you know?

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*Recall number bonds to 10 and reason

about associated facts e.g. 6+4=10

therefore 4+6=10 and 10-6=4

Show that addition of two numbers can be

done in any order

Show that subtraction of one number from

another cannot be done in any order

*Add a two-digit number and ones and a

two-digit number and tens within 100,

where no regrouping is required,

explaining their method verbally, in

pictures or using apparatus and jottings

*Subtract a two-digit number and ones and

a two-digit number and tens within 100,

where no regrouping is required,

explaining their method verbally, in

pictures or using apparatus and jottings

**Recall all number bonds to and within 10 and

use these to reason with and calculate bonds to

and within 20

Recognise and use the inverse relationship

between addition and subtraction

Begin to add three one-digit numbers using

knowledge of number pairs

e.g. 7 + 3 + 5 = 10 + 5 = 15

Use the vocabulary related to addition and

subtraction including sum and difference

**Add any two two-digit numbers within 100

including the use of apparatus and/or jottings,

such as empty number line

**Subtract any two two-digit numbers within

100 with the use of apparatus and/or jottings,

such as empty number line

Recall and use addition and subtraction facts to 20

Use related facts (facts to 10, facts to 20) to derive

addition and subtraction facts to 100 e.g. 60 + 40 = 100;

100–40 = 60

Add three one-digit numbers using knowledge of

number pairs e .g. 8 + 9 + 2 = 10 + 9 =19

Use estimation to check that an answer to a calculation

is reasonable

Solve simple word problems involving

addition / subtraction using the strategies

outlined above

Solve simple number problems, including missing number problems, that involve all of the above

Solve simple word problems involving

addition/subtraction using the strategies outlined

above

Solve number problems, including missing number

problems, that involve all of the above

Begin to reason about addition and subtraction

e.g. True or false? The sum of two odd numbers

will always be even. How do you know?

Solve one step word problems involving addition /

subtraction using the strategies outlined above

Solve number problems, including missing number

problems, and puzzles that involve all of the above

***Reason about addition and subtraction e.g. True or

false? The sum of three odd numbers will always be odd.

How do you know?

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Calculate mathematical statements with known multiples (2s, 5s and 10s) and begin to write them using the x, ÷ and = signs

Recall and use multiplication facts for the

2 times table

Recall and use division facts for the 2

times table

Represent multiplication as arrays using

known multiples (2s, 5s and 10s)

Recall and use doubling and halving facts

for numbers up to double 10

Recognise odd and even numbers to 20

and relate to multiples/groups of two,

using practical resources to support

Calculate mathematical statements with known multiples and write them using the x, ÷ and = signs

Recall and use multiplication facts for the 10

times table

Recall and use division facts for the 10 times

table

Represent multiplication as arrays and as

repeated addition using known multiples

(2s, 5s and 10s)

**Demonstrate an understanding of

commutativity e.g. 2 x 10 =20 so 10 x 2 =20

Recall the doubles of some multiples of 10 (e.g.

double 20 is 40) and recall the related halves

(e.g. half of 40 is 20)

Recognise odd and even numbers to at least 20

and relate to multiples/groups of two

**Recall and use multiplication facts for the 2, 5 and 10

times tables

**Recall and use division facts for the 2, 5 and 10 times

table

Use informal methods, such as empty number, lines for

multiplication using known multiples (2s, 3s, 5s and 10s)

Use informal methods, such as empty number lines, for

division using known multiples (2s, 3s, 5s and 10s)

Recall the doubles of multiples of 10 to 100 (e.g. double

30 is 60) and recall the related halves

(e.g. half of 60 is 30)

Recognise odd and even numbers within 100 and relate

to multiples/groups of two




Solve simple word problems involving known multiples, using practical resources, informal written methods (including pictures and arrays), related vocabulary and beginning to use appropriate signs

Solve simple word problems involving known multiples, using practical resources, informal written methods (including pictures and arrays), related vocabulary and using appropriate signs

Solve missing number problems, involving the above

**Use multiplication and division facts for the 2, 5 and 10 x tables to solve simple problems

Solve problems, including missing number problems, involving the above

Solve problems involving odd/even numbers

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Recognise, find and name a half as one of two equal parts of an object or shape and

use fraction notation 1

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Find half of a set of objects with numbers to at least 20 using practical resources and link to equal sharing and grouping

Recognise, find and name a quarter as one of four equal parts of an objects or shape

and use fraction notation 1

4

Find a quarter of a set of objects with numbers to at least 20 using practical resources

Find 1

2 and

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4 of a length, set of objects or

quantity using fraction notation including with

the use of practical resources and link to equal

sharing and grouping

Begin to recognise and write the non-unit fraction 3

4 using diagrams and resources

**Identify fractions 𝟏

𝟒 ,

𝟏

𝟑 ,

𝟏

𝟐 ,

𝟐

𝟒 and

𝟑

𝟒 of a shape and

know that all parts must be equal parts of the whole

**Identify 𝟏

𝟒 ,

𝟏

𝟑 ,

𝟏

𝟐 ,

𝟐

𝟒 and

𝟑

𝟒 of a number e.g. a

length, set of objects or quantity ( including with the

use of practical resources and diagrams)

Recognise the equivalence of 1

2 and

2

4 using simple

diagrams and resources

Solve simple problems, including word problems, which involve fractions, using concrete objects and pictorial representations to support

Solve problems, including word problems, that involve all of the above, using concrete objects and pictorial representations to support

Solve problems, including word problems, using concrete objects and pictorial representations to support

***Reason about fractions e.g. would you rather have 𝟏

𝟐 of 12 sweets or

𝟏

𝟒 of 20 sweets? Why?

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Use metre and centimetre to estimate and measure length and height

Compare lengths using longer/shorter, longer than/shorter than

Confidently read the time to the hour and half past the hour using an analogue clock

Know days of the week, months of the year

*Recognise and know the value of all denominations of all coins including £2

Recognise and know the value of £5 and £10 notes

Recognise the symbols for pounds (£) and pence (p)

Use litre and millilitre to estimate and measure capacity and kilogram and gram to estimate and measure mass

Compare capacity and mass using more/less, heavier/lighter

Understand °C as a unit of measurement for temperature

**Read scales in divisions of twos, fives and tens

where all the numbers are given

**Read the time on an analogue clock to the

nearest 15 minutes ( including quarter past and quarter to the hour)

Recognise and know the value of all coins, and notes up to £20

Recognise and use symbols for pounds (£) and pence (p)

**Use different coins to make the same amount

Begin to read scales in divisions of twos, fives and tens

Choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales and measuring vessels

***Read scales in divisions of twos, fives and tens

where not all the numbers are given

Compare and order lengths, mass, volume/capacity and record the results using >, < and =

Read °C on a thermometer to the nearest appropriate unit (positive temperatures only)

***Read the time to the nearest five minutes on an

analogue clock

Know the number of minutes in an hour and the number of hours in a day

Know the relationship between £ and p

Solve simple problems in a practical context using m and cm

Solve simple problems (including word problems) in the context of money including giving change from 20p

Solve problems involving finding different combinations of coins that equal the same amounts of money (within 20p)

Solve simple problems in a practical context using kg and g; l and ml

Solve simple problems (including word problems) in the context of money including giving change from 50p

**Solve problems involving finding different combinations of coins that equal the same amounts of money (within 50p and then £1)

Solve problems, including word problems, that involve the above

Solve simple problems involving the passage of time

Solve simple problems in a practical context involving addition and subtraction of money, including giving change from £1

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*Recognise and name common 2-D

shapes as outlined in Year 1 and describe some of their properties using number of sides and corners

Recognise 2-D shapes in different orientations

Sort 2-D shapes according to their properties e.g. the number of sides

Recognise line symmetry in 2-D shapes in practical contexts

*Recognise and name 3-D shapes as outlined in

Year 1 and describe some of their properties in terms of number of faces and vertices

Begin to recognise 2-D shapes on the surface of 3D-shapes, e.g. a square or a rectangle on a cuboid

Compare and sort common 2-D and 3-D shapes (including everyday objects) according to their properties

Recognise line symmetry in a vertical line

**Name 2-D shapes and describe their properties

(extend with pentagon and hexagon), including the number of sides, and lines of symmetry

Recognise right angles in 2-d shapes

**Name 3-D shapes and describe their properties,

including the number of edges, vertices and faces

Confidently compare and sort common 2-D and 3-D shapes according to their properties

Identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid

Begin to reason about 2D shapes e.g. compare a rectangle and a triangle - find one thing that is the same about them; find one thing that is different

Begin to reason about 3D shapes e.g. compare a cuboid and a triangular prism - find one thing that is the same about them; find one thing that is different

***Reason about shapes by describing similarities and

differences, using their properties e.g. what is the same about these two shapes; what is different about these two shapes?

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Use the full range of vocabulary to describe position and movement in a straight line (left, right, forwards, backwards, between, middle, in front of, behind, up, down)

Use mathematical vocabulary to describe turns using whole, half, quarter and three quarters in practical contexts; use the vocabulary clockwise and anti-clockwise in practical contexts

Order and arrange combinations of shapes in patterns and sequences

Describe rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti-clockwise), including in practical contexts such as programming robots using instructions given in right angles



Asterisk* refers to the Teacher Assessment Framework standards: Working towards * Working at ** Greater depth***


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Interpret simple tables and pictograms

Begin to construct simple pictograms

Interpret simple tally charts

Interpret and construct simple block diagrams with scales in divisions of ones

Begin to interpret simple block diagrams with scales in divisions of twos where all numbers on the scale are given

**Interpret simple block diagrams with scales in

divisions of ones, twos, fives and tens where all numbers on the scale are given

Interpret and construct simple pictograms, tally charts, block diagrams and tables

***Interpret simple block diagrams with scales in

divisions of ones, twos, fives and tens where not all the numbers on the scale are given, estimating points in between

Understand and interpret pictograms with simple scales e.g. where one face represents 2 children/ one book represents 5 books

Solve simple one-step questions by counting the number of objects in each category presented in simple tables and pictograms, such as ‘How many…?

Solve simple one-step questions using information presented in tally charts and block diagrams

Solve one-step questions (including questions using totalling and comparing) using information presented in block diagrams, pictograms, tally charts and tables


***Solve word problems that involve more than one step

***Solve more complex missing number problems e.g. 27 +23 = 20 + 10 +

***Use reasoning about numbers and relationships to solve more complex problems and explain their thinking

***Use multiplication and division facts to make deductions outside known multiplication facts e.g. 16 x 5

Work systematically

Follow a simple line of enquiry

Identify patterns and relationships

Reason mathematically e.g. responds to ‘How do you know?’ questions


Grasp new concepts quickly




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Read and write numbers to 200 in numerals

and words

Count from 0 (forwards and backwards) in multiples of 3 and 4 to the 12

th multiple

Identify the number that is ten more or less within 200

Order and compare (using < and > signs) numbers up to 200

Recognise the place value of each digit in a three-digit number to 200, including with the use of practical resources

Read and write numbers to 500 in numerals and words

Count from 0 (forwards and backwards) in multiples of 4, 8 and 50 to the 12

th multiple

Identify the number that is ten or one hundred more or less than a given number within 500

Order and compare (using < and > signs) numbers up to 500

Recognise the place value of each digit in a three-digit number to 500, including with the use of practical resources

Read and write numbers to 1,000 in numerals and words

Count from 0 (forwards and backwards) in multiples of 4, 8, 50 and 100 to the 12

th multiple

Identify the number that is ten or one hundred more or less than a given number within 1,000

Order and compare (using < and > signs) numbers up to 1,000

Recognise the place value of each digit in a three-digit number to 1,000


Reason about number and place value e.g. If you wrote these numbers in order starting with the smallest number, which would come third? 200, 105, 150, 195, 159. How do you know?


Reason about number and place value e.g. If you wrote these numbers in order starting with the largest, which number would be third? 250, 500, 205, 195, 495. Explain how you ordered these numbers


Reason about number and place value e.g. what is wrong with this sequence of numbers? 650, 600, 500, 450, 400. Explain how you know

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Mentally add a three-digit number and ones

and a three-digit number and tens within 200,

including the use of jottings such as a number

line

Mentally subtract ones/tens from a three-digit

number within 200, including the use of

jottings such as a number line

Use a range of mental strategies to add and

subtract (for example, add 9 to a two-digit

number by adding 10 and adjusting)

Add and subtract two two-digit numbers,

bridging 100, using informal written methods,

such as an empty number line or partitioning

Mentally add a three-digit number and ones;

tens; hundreds within 500, including the use of


Mentally subtract from a three-digit number

ones; tens; hundreds within 500, including the

use of jottings such as a number line


subtract (for example, add 19 to a two-digit or

three-digit number by adding 20 and adjusting,

find the small difference by counting on)

Begin to use the formal written method to add

two two-digit numbers

Begin to use the formal written method to

subtract two two-digit numbers

Mentally add a three-digit number and ones;

tens; hundreds within 1,000, including the use of


Mentally subtract from a three-digit number

ones; tens; hundreds within 1,000, including the



subtract (for example, add 99 to a two-digit or

three-digit number by adding 100 and adjusting)

Add numbers with up to three digits using the

formal written method

Subtract numbers with up to three digits using

the formal written method

Solve one- step word problems involving

addition / subtraction using the methods

outlined above

Solve number problems, including missing

number problems, that involve the above

Reason about addition and subtraction e.g. True or false? If you add 5 to a number ending in 6 the answer will have 1 in the units’ column. How do you know?

Solve one- step word problems involving

addition / subtraction using the methods

outlined above


number problems, that involve the above

Reason about addition and subtraction e.g. .Is it always, sometimes or never true that if you subtract a multiple of 10 from any number the units digit of that number stays the same. How do you know?

Solve one- step and two-step word problems

involving addition / subtraction using the

methods outlined above


number problems, and puzzles that involve the

above

Reason about addition and subtraction

e.g. Is it always, sometimes or never true that

the difference between two odd numbers is

odd? How do you know?

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times table, up to the 12th multiple


table up to the 12th multiple

Use informal methods such as empty number

lines or arrays for multiplication, using known

times tables

Use informal methods such as empty number

lines or arrays for division, using known times

tables


times tables up to the 12th multiple


tables up to the 12th multiple

Multiply a teen number by a one-digit number

using an informal method such as partitioning

or the grid method, with known multiples e.g.

13 x 4

Begin to use the formal written layout for

division using known times tables

Begin to determine remainders using known

facts

Recall and use multiplication facts for the 3, 4

and 8 times tables up to the 12th multiple

Recall and use division facts for the 3, 4 and 8

times tables up to the 12th multiple

Multiply a teen number by a one-digit number

using the formal written method, with known

multiples e.g. 14 x 3; 18 x 4

Understand and use the commutative properties

of multiplication and the inverse relationship

between multiplication and division

Use the formal written layout for division using

known times tables e.g. 32 divided by 4

Determine remainders using known facts

e.g. recognise that 25 divided by 8 will give a

remainder of 1

Solve word problems involving multiplication / division using the methods outlined above

Solve problems, including missing number problems, involving the above e.g. x 3 = 24


Solve problems, including missing number problems, involving all of the above e.g.

24 = x Which pairs of numbers could be written in the boxes? Solve simple correspondence problems e.g.

how many different outfits can you make with two different hats and two different coats; two different hats and three different coats; three different hats and three different coats?


Solve problems, including missing number problems, involving all of the above e.g. 15 x = 45

Solve simple positive integer scaling problem e.g. my sunflower is 40cm tall. Your sunflower is twice as tall/ three times as tall. How tall is your sunflower?




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ctio

ns

Count up and down in tenths, using practical

resources such as a counting stick

Recognise, find and write unit fractions with

small denominators, such as 1/5, using

practical resources and diagrams to support

Find unit fractions, with small denominators,

of a number and a discrete set of objects, by

connecting finding unit fractions to division

Begin to recognise and write non-unit

fractions using diagrams to support e.g. 2/3

Begin to recognise and show, using diagrams

to support, simple equivalent fractions of a

half

Recognise that tenths arise from dividing an

object into 10 equal parts using practical

resources and diagrams

Recognise, find and write non-unit fractions,

with small denominators, such as 2/3, 3/5,

using practical resources and diagrams to

support

Begin to find non-unit fractions, with small

denominators, of a number and a discrete set

of objects using resources to support e.g. 2/3

of 15

Recognise and show, using diagrams to

support, simple equivalent fractions of a half

e.g. 1/ 2 = 5/10

Compare unit fractions, using diagrams such

as a fraction wall to support e.g. 1/ 4 > 1/8

Add fractions with the same denominator

within one whole e.g. 3/10 + 4/10

Recognise, find and write fractions of a number

and a discrete set of objects, including unit

fractions and non-unit fractions (with small

denominators), using diagrams and resources to

support e.g.1/5 of 50, 2/5 of 30

Recognise and use fractions as ordered numbers

on a 0-1 number line

Recognise and show, using diagrams to support, a

range of simple equivalent fractions with small

denominators such as 1/3 = 2/6, 4/8 = 1/2

Order a set of unit fractions, using diagrams such

as a fraction wall to support

Compare and order non-unit fractions with the

same denominators, using diagrams such as a

fraction wall to support

Add and subtract fractions with the same

denominator within one whole

e.g. 7/8- 3/8

Solve problems, including word problems, that involve fractions

Reason about fractions e.g. would you rather have 1/2 of £24 or 1/3 of £30? Why?


Reason about fractions e.g. True or false? 1/3 > 1/ 2. How do you know?


Reason about fractions e.g. would you rather have 2/3 of 18 cherries or 1/5 of 45 cherries? Why?

Me

asu

rem

en

t

Know and use the relationship between m and cm

Measure and compare: lengths (m/cm); mass (kg/g); volume/capacity (l/ml) in practical contexts

Add and subtract amounts of money within £2, in practical contexts, including giving change

Tell and write the time to the nearest five minutes on an analogue clock, including clocks with Roman numerals from I to XII

Tell and write the time to the nearest five minutes on a 12-hour digital clock

Begin to use a.m., p.m., noon/midday and midnight when telling the time

Know the number of seconds in a minute

Know and use the relationship between cm and mm

Measure, compare, add and subtract measurements in practical contexts, including mixed units of measurement (1m and 35cm)

Understand the term perimeter and begin to measure the perimeter of simple 2-D shapes


Tell and write the time to the nearest five minutes from an analogue clock, including clocks with Roman numerals from I to XII, and from 12-hour digital clocks with accuracy

Use a.m., p.m., noon/midday and midnight when telling the time

Know the number of days in a year and in a leap year

Know and use the relationship between m and mm

Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml) including mixed units of measurement with accuracy

Measure the perimeter of simple 2-D shapes


Tell and write the time to the nearest minute from an analogue clock, including clocks with Roman numerals from I to XII, and from 12-hour digital clocks

Know the number of days in each month

Solve problems, including word problems, that involve measurement, including time

Solve problems, including word problems, that involve measurement, including time

Solve problems, including word problems, that involve all measurement, including time

Reason about measurement by following a simple line of enquiry e.g. my height measures the same as my reach. True or false? All 8 year olds can jump more than one metre. True or false? How will you find out?

Ge

om

etr

y

Pro

pe

rtie

s o

f sh

ape

Identify right angles in shapes and recognise that a right angle is equivalent to a quarter turn

Begin to identify whether angles are greater or less than a right angle

Identify and describe 2-D shapes using their properties (for example including the number of sides, a line of symmetry, number of right angles)

Draw 2-D shapes

Begin to identify horizontal and vertical lines

Recognise that two right angles make a half turn

Identify whether angles are greater or less than a right angle

Recognise 3-D shapes and describe them

using their properties, including the number

of edges, vertices and faces

Identify 2-D shapes on the surface of a wider

range of 3-D shapes e.g. triangular faces on a

tetrahedron

Make 3-D shapes with modelling materials

e.g. using Polydron, using known properties

Recognise that three right angles make three quarters of a turn and that four make a complete turn

Identify whether angles are greater or less than a right angle, using the terms acute and obtuse

Describe the properties of 2-D shapes using accurate language, including lengths of lines, obtuse/acute angles and whether a shape is symmetrical or non-symmetrical

Identify horizontal and vertical lines and pairs of perpendicular and parallel lines

Reason about shapes e.g. what is the same about these three shapes; what is different about these three shapes?

Reason about shapes e.g. which of these

shapes is the odd one out? Why?

Reason about shapes e.g. True or false? The only polygons which have right angles are rectangles. Explain your decision

Stat

isti

cs

Collect and interpret data using tables and tallies

Present data using bar charts and pictograms using simple scales such as 2 units per cm in bar charts

Interpret bar charts and pictograms using simple scales

Present data using bar charts, pictograms and tables and use simple scales such as 5 units per cm in bar charts

Interpret bar charts and pictograms using simple scales

Understand and use simple scales (for example units of 2, 5, 10 ) to construct and interpret in pictograms and bar charts with increasing accuracy



Solve one-step questions (for example, ‘How many more?’ and ‘How many fewer?’) using information presented in tables, scaled bar charts and pictograms

Begin to solve two-step questions using information presented in tables, scaled bar charts, pictograms

Solve one-step and two-step questions using information presented in scaled bar charts, pictograms and tables in different and varied contexts, such as through science

Collect, present and interpret data by following a simple line of enquiry e.g. which colour car is the most popular? How will you find out? How will you present your findings?



Work systematically

Follow a simple line of enquiry

Identify patterns and relationships

Make predictions

Reason mathematically e.g. respond to ‘Explain how you know’


Grasp new concepts quickly

Make links between areas of learning





Nu

mb

er

–

Co

un

tin

g a

nd

Pla

ce V

alu

e

Read and write numbers to at least 2,000 in

numerals and words

Count, forwards and backwards, in multiples of 3, 4, 6, 8, 50 and 100

Identify the number that is one hundred more or less than a given number to at least 2,000

Order and compare numbers to at least 2,000

Round two and three-digit numbers to the nearest 10

Recognise the place value of each digit in a three-digit number and in a four-digit number

Read Roman numerals 1-12 (I to XII) in the context of time

Read and write numbers to at least 5,000 in numerals and words

Count, forwards and backwards, in multiples of 9 and 25

Identify the number that is ten or one hundred more or less than a given number to 5,000.

Order and compare numbers to 5,000

Round three-digit and four-digit numbers to the nearest 10 or 100

Recognise the place value of each digit in a four-digit number to at least 5,000

Read Roman numerals to 50 (L)

Read and write numbers to 10,000 in numerals and words and recognise the place value of each digit, including zero as a place holder

Count, forwards and backwards, in multiples of 6, 7, 9, 25 and 1000

Count backwards through 0 to include negative whole numbers

Identify the number that is ten, one hundred or one thousand more or less than a given number to 10,000

Order and compare numbers within 10,000

Round three and four-digit numbers to the nearest 10, 100 or 1000

Read Roman numerals to 100 ( C)

Solve number and word problems that involve the above

Reason about numbers and place value e.g. If you wrote these numbers in order starting with the smallest, which number would be third? 950, 999, 905, 995, 959. Explain how you ordered these numbers


Reason about numbers and place value e.g. If you wrote these numbers in order starting with the largest, which number would be third? 1,203 1,023 3,201 2,310, 3,021. Explain how you ordered these numbers


Reason about numbers and place value e.g. a number rounded to the nearest ten is 890. What is the smallest/largest number it could be? Explain how you know

Nu

mb

er

–

Ad

dit

ion

an

d S

ub

trac

tio

n

Mentally add a three-digit number and a two-

digit number, including with the use of jottings

such as a number line

Mentally subtract a two-digit number from a

three-digit number, including with the use of


Add two three-digit numbers using the formal

written method

Subtract two three-digit numbers using the

formal written method

Mentally add and subtract numbers with up to

three-digits, including with the use of jottings

such as a number line

Add two four-digit numbers using the formal

written method

Subtract four-digit numbers using the formal

written method

Mentally add and subtract numbers with up to four-

digits, using a range of strategies, including with the


Use estimation and inverse operations to check

calculations

Add and subtract numbers with up to 4 digits,

including decimal numbers with up to two decimal

places (initially in the context of money or measures),

using the formal written methods

Solve addition and subtraction one-step and

two-step word problems (including simple

money problems) using the above, deciding

which operations to use

Solve number problems, including empty box


Reason about addition and subtraction e.g. .Is it always, sometimes or never true that if you subtract a multiple of 100 from any three-digit number the tens digit of that number stays the same. How do you know?

Solve addition and subtraction one and two-

step word problems (including money

problems) using the above, justifying methods

chosen

Solve number problem, including empty box


Reason about addition and subtraction e.g.

which questions are easy/ more challenging?

452 + 235; 387 + 279; 999- 555; 702 – 384.

Explain why

Solve addition and subtraction one-step and two-step

word problems (including money and measure

problems with up to two decimal places) using the

above, deciding which operations to use and

justifying methods chosen

Solve number problems, including empty box

problems, that involve the above

Reason about addition and subtraction e.g. is it

always, sometimes or never true that the sum of four

even numbers is divisible by 4? How do you know?

Nu

mb

er-

Mu

ltip

licat

ion

an

d D

ivis

ion


times table up to the 12th multiple


tables to the 12th multiple

Multiply whole numbers by ten

Divide whole numbers by 10 (with whole

number answers e.g. 420 ÷ 10)

Recognise and use commutatively in mental

calculations for multiplication

Understand the effect of multiplying numbers

by 0 and 1 and dividing numbers by 1

Using known multiplication facts, multiply

mentally (with jottings) a two-digit number by a

one-digit number using the distributive law

(partitioning)

Using known multiplication facts, multiply any

two-digit number by a one-digit number using

the formal written method

Using known facts, use the formal written

layout for division, including examples with

remainders e.g. 48 divided by 6; 37 divided by 4

Recall and use multiplication facts for the 7 and

9 times tables up to the 12th multiple

Recall and use division facts for the 7 and 9

times tables to the 12th multiple

Use known multiplication and division facts

and place value to derive other related facts

Multiply numbers by ten (including numbers

with one decimal place)

Divide whole numbers by 10 (including answers

with one decimal place)

Recognise factor pairs

Use a mental method, such as partitioning, to

divide a two-digit numbers by a single-digit

number e.g. 56 divided by 4

Multiply any two-digit number by any one-digit

number using formal written method of short

multiplication

Use the formal written method of short division

to divide any two-digit number by any one-digit

number, including examples with remainders

Recall and use multiplication facts for all times tables

up to 12 x 12

Recall and use division facts for all times tables up to

12 x 12

Use multiplication and division facts and place value

to derive other related facts

Multiply numbers by ten and one hundred, including

numbers with one decimal place

Divide whole numbers by ten and one hundred,

including answers with one decimal place

Use a range of mental methods to multiply and divide,

such as factor pairs to aid multiplication

e.g.4 x 24 = 4 x 2 x 12 = 8 x 12 = 96

Multiply two-digit or three-digit numbers by a one-digit number using the formal written method of short multiplication

Use the formal written method of short division to

divide any two- digit or three-digit number by a one-

digit number, including examples with remainders

Solve word problems involving multiplication/ division using methods outlined above

Solve number problems, including empty box problems, that involve the above

Solve integer scaling problems

Reason about multiplication e.g. If 7 x 6 = 42, how could use this fact to solve 70 x 6?

Solve word problems involving multiplication/ division using methods outlined above

Solve number problems, including empty box problems, that involve the above

Solve correspondence problems

Reason about multiplication/division e.g. If you know 9 x 6 = 54, what other facts do you know?

Solve word problems involving multiplication/division using the methods outlined above

Solve number problems and puzzles that involve all of the above

Reason about multiplication/division e.g. how would you use this fact, 42 ÷ 6 = 7, to solve 84 ÷ 6 =?




Nu

mb

er

–

Frac

tio

ns

an

d d

eci

mal

s

Recognise and show, using diagrams to

support, families of common equivalent

fractions for 1/ 2

Add and subtract fractions with the same

denominator within one whole, confidently

Find unit and non-unit fractions with small

denominators of numbers and a discrete sets of

objects, using diagrams and resources to

support e.g. 1/8 of 32 apples, 3/8 of 32 apples

Understand that tenths arise by dividing an

object into ten equal parts and record one

tenth as 1

10 and 0·1

Begin to understand place value in numbers

with one decimal place

Begin to compare and order numbers with one

decimal place

Recognise and write the decimal equivalent for

1/ 2

Understand the effect of dividing a one-digit

number by 10

Identify hundredths in contexts such as money

and length and use decimal notation e.g.

145cm = 1.45 m; 268p = £2.68

Recognise and show, using diagrams to support,

families of common equivalent fractions e.g. 1/ 4 and

1/3

Add fractions with the same denominator, beginning to

include examples where the total is greater than one

whole

Subtract fractions with the same denominator,

beginning to include crossing one whole

Find unit and non-unit fractions of numbers and

quantities, using diagrams and resources to support;

begin to relate to multiplication and division

Recognise and write decimal equivalents of any

number of tenths e.g. 2

10 = 0·2

Understand place value in numbers with one decimal

place

Begin to round decimals with one decimal place to the

nearest whole number

Compare and order numbers with one decimal place

Recognise and write the decimal equivalent for 1/ 4

Understand the effect of dividing a one-digit or two-

digit whole number by 10

Understand that hundredths are an object divided by

100 and record one hundredth as 1

100 and 0·01

Recognise and show, using diagrams to support, families of common equivalent fractions e.g. 3/ 4 or 2/3

Add fractions with the same denominator, including where the total is greater than one whole

Subtract fractions with the same denominator, including crossing one whole

Find unit and non-unit fractions of numbers and quantities; relate to multiplication and division

Recognise and write decimal equivalents of any number of tenths or hundredths

Recognise and write the decimal equivalent for 3/ 4

Understand the effect of dividing a one-digit or two-digit whole number by 100

Understand place value in numbers with one and two decimal places

Round decimals with one decimal place to the nearest whole number

Compare and order numbers with the same number of decimal places up to two decimal places

Solve problems, including word problems, that involve fractions, as above

Reason about fractions e.g. would you rather have 2/5 of 30 cherries or 2/3 of 21 cherries? Why?

Solve problems, including word problems, that involve fractions, as above

Begin to solve simple measure and money problems involving decimals to two decimal places

Reason about fractions e.g. True or false? 7/10 > 3/5. How do you know?

Solve problems using fractions to calculate quantities, including non-unit fractions where the answer is a whole number

Solve simple measure and money problems involving fractions and decimals to two decimal places

Reason about fractions and decimals e.g. put these numbers in order starting with the smallest: 0.75, 1/ 4, 5/10, 60/100. Explain how you ordered the numbers

Me

asu

rem

en

t

Begin to use the relationship between units of measure to convert

Measure the perimeter of rectangles (including squares) in centimetres and/or metres

Estimate and measure using different measures, including mixed units of measurements

Record measures beginning to use decimal notation, in practical contexts

Read and write analogue and digital time (12 hour) to the nearest minute; convert between analogue and digital time; continue to use a.m. and p.m.

Use the relationship between metric units of measure and units of time to convert

Calculate the perimeter of rectangles and other rectilinear shapes where the lengths of sides are given

Find the area of rectangles by counting squares

Estimate and begin to calculate using different measures, including mixed units of measurements

Record measures using decimal notation

Begin to convert time between 12 and 24 hour clocks

Use the relationship between metric units of measure and time to convert, confidently

Measure and calculate the perimeter of any rectangle or other rectilinear shape in centimetres and/or metres

Express the formula for finding the perimeter of a rectangle in words

Relate the area of rectangles to arrays and multiplication

Estimate, compare and calculate using different measures

Read, write and convert time between analogue and digital time

Read, write and convert time between 12 and 24 hour clocks

Solve problems, including word problems, using a

range of metric measures

Solve problems, including word problems, in the

context of money

Reason about measurement e.g. If you put these

lengths in order, which would come third? 1.54m,

999mm, 95cm, 1m 60cm, 1.05 m. How do you

know?

Solve problems using knowledge of the relationship between hours and minutes; minutes and seconds; years and months; weeks and days

Solve problems using a range of metric measures and money, as above

Reason about measurement e.g. Tom says that 8.35 am is closer to 8.00am than 9.00am. Is he right? How do you know?

Solve more challenging problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days

Solve problems using a range of metric measures and money, as above

Reason about measurement e.g. 2500g, 1.75kg, 1kg 500g, ½ a kg, 600g, if you put these in order which one will be third. How did you work it out?



Ge

om

etr

y

Po

siti

on

an

d d

ire

ctio

n

Begin to read coordinates on a 2-D grid in the first quadrant

Describe positions on a 2-D grid as coordinates in the first quadrant

Plot given coordinates on a 2-D grid in the first quadrant

Plot specified points and draw sides to complete a given polygon using coordinates in the first quadrant

Begin to describe movements between positions as translations of a given unit to the left/right and up/down using co-ordinates in the first quadrant

Stat

isti

cs

Interpret and present discrete data using appropriate graphical methods including bar charts

Interpret a range of scales, for example units of 2, 5, 10 reading unmarked divisions confidently

Interpret and present discrete data using appropriate graphical methods and a greater range of scales, for example 2, 5, 10, 20, 25

Begin to interpret and present continuous data using appropriate graphical methods such as time graphs

Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs

Interpret and use a greater range of scales with increasing accuracy

Solve simple comparison, sum and difference problems using information presented in bar charts, pictograms and tables, using the above

Solve comparison, sum and difference problems using information presented in bar charts, pictograms and tables, using the above

Solve comparison, sum and difference problems using information presented in bar charts, pictograms and tables, confidently and accurately

Collect, present and interpret data by following a line of enquiry



Work systematically; record results in an organised way

Reason mathematically by following a line of enquiry

Identify patterns and relationships; make predictions and simple generalisations


Make justifications e.g. why they chose a method, how they know they are correct

Grasp new concepts quickly; make links between areas of learning


Ge

om

etr

y

P

rop

ert

ies

of

shap

e

Identify regular and irregular geometric shapes including quadrilaterals and triangles

Identify different types of triangles (isosceles, equilateral, scalene and right angled)

Identify acute, obtuse and right angles (without using a protractor)

Complete a simple symmetric figure with respect to a horizontal or vertical line of symmetry, where the line of symmetry dissects the figure/shape

Identify different types of quadrilaterals (rhombus, parallelogram, trapezium)

Begin to Identify lines of symmetry in 2-D shapes with more than one line of symmetry

Complete a simple symmetric drawing where the line of symmetry does not dissect the original shape

Compare and classify geometric shapes including different quadrilaterals and triangles, based on their properties and sizes

Compare and order angles up to 180°, without using a protractor

Identify all lines of symmetry in 2-D shapes, including shapes presented in different orientations

Complete a simple symmetric figure with respect to a specific line of symmetry, with confidence

Reason about 2-D shapes e.g. Tariq says that he can draw a right-angled triangle which has another angle that is obtuse. Is he right or wrong? Explain how you know?

Reason about 2-D shapes e.g. What is the same about these quadrilaterals; what is different about them?

Reason about 2-D shapes e.g. all quadrilaterals have at least one line of symmetry. True or false? How do you know?




Nu

mb

er

–

Co

un

tin

g a

nd

Pla

ce V

alu

e

Read and write numbers to 100,000

Given a number, identify the number that is ten, one hundred or one thousand more or less within 100,000


Round any number within 100,000 to the nearest 10, 100 or 1000

Recognise the place value of each digit in a five-digit number

Read and write numbers to 500,000

Given a number, identify the number that is ten, one hundred, one thousand or one hundred thousand more or less within 500,000


Round any number up to 500,000 to the nearest 10, 100, 1,000 or 10,000

Recognise the place value of each digit in a six-digit number to 500,000

Count forwards and backwards with positive and negative whole numbers, including through zero

Read Roman numerals to 1,000 (M)

Read and write numbers to 1,000,000 (one million) and determine the value of each digit

Given a number, identify the number that is ten, one hundred, one thousand, ten thousand or one hundred thousand more or less within 1,000,000

Order and compare numbers within 1,000,000

Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 or 100,000

Interpret negative numbers in context e.g. temperature

Read Roman numerals to 1,000 (M) and begin to recognise years in Roman numerals e.g. this year (MMXVIII)


Reason about numbers and place value e.g. a number rounded to the nearest 100 is 8,900. What is the largest/smallest number it could be? How did you work it out?


Reason about numbers and place value e.g. a number rounded to the nearest 1,000 is 25,000. What is the largest/smallest number it could be? How did you work it out?


Reason about number and place value e.g. 560,000 65,000 56,000 506,000 605,000 650,000 If you put these five numbers in order, starting with the smallest, which one would come third? Explain how you ordered the numbers

Nu

mb

er

–

Ad

dit

ion

an

d S

ub

trac

tio

n

Mentally add two numbers with up to 4

digits (including decimal numbers with one

decimal place), with the use of jottings such

as a number line

Mentally subtract numbers with up to 4 digits (including decimal numbers with one decimal place), with the use of jottings such as a number line

Add numbers with up to 4 digits, including decimal numbers with up to two decimal places, using the formal written method

Subtract whole numbers with up to 4 digits, including numbers with up to two decimal places, using the formal written method

Mentally add two numbers with up to 5 digits

(including decimal numbers), with the use of


Mentally subtract two numbers with up to 5 digits

(including decimal numbers), with the use of


Add numbers with up to 5 digits ,including examples with decimal numbers with up to two decimal places, using the formal written method

Subtract whole numbers with up to 5 digits, including examples with decimal numbers up to two decimal places, using the formal written method

Add numbers mentally, with the use of jottings, with increasingly large numbers and using a range of strategies

Subtract numbers mentally, with the use of jottings, with increasingly large numbers and using a range of strategies

Add numbers with up to 5 digits, including decimal numbers with up to three decimal places, using the formal written method

Subtract whole numbers with up to 5 digits, including numbers with up to three decimal places, using the formal written method

Solve addition and subtraction one-step and two-step word problems, using the above methods, deciding which operations to use and justifying chosen methods

Reason about addition/subtraction e.g. Is it always, sometimes or never true that if you subtract a multiple of 1,000 from any four-digit number the hundreds digit of that number stays the same. How do you know?

Solve addition and subtraction two-step problems word problems, using the above methods, deciding which operations to use and justifying methods chosen

Solve number problems, including missing problems, that involve the above

Reason about addition/subtraction e.g. two four-digit whole numbers total 14,843. What numbers could they be? Convince me!

Solve addition and subtraction two-step and multi-step word problems in context, using the above methods

Solve number problems and puzzles that involve the above

Reason about addition subtraction e.g. the sum of two consecutive numbers gives a total that is a prime number. Is this always true, sometimes true or never true?

Nu

mb

er-

M

ult

iplic

atio

n a

nd

Div

isio

n

Recall and use multiplication facts for all

times tables up to 12 x 12, with increasing

confidence

Recall and use division facts for all times

tables up to 12 x 12, with increasing

confidence

Find factor pairs of a number

Recognise and use some square numbers and the notation for squared (²)

Multiply numbers by ten or one hundred,

including numbers with one or two decimal

places

Divide whole numbers by ten and one

hundred, including answers with one or two

decimal places

Multiply three-digit and four-digit numbers by a one-digit number using the formal written method of short multiplication

Divide three-digit numbers by a one-digit number using the formal written method of short division with whole number answers and answers with remainders

Find all factor pairs of a number

Recognise and use square numbers and the notation for squared (²) up to 12 x 12

Begin to understand and use the vocabulary of prime numbers; recall some prime numbers up to 19

Multiply numbers by ten, one hundred and one thousand, including numbers with one or two decimal places

Divide whole numbers by ten, one hundred and one thousand, including answers with one or two decimal places

Multiply and divide numbers mentally drawing on known facts and using factor pairs

Begin to multiply a two-digit number by a two-digit number using the formal written method of long multiplication

Divide three-digit numbers by a one-digit number

and by 11 and 12, using the formal written method

of short division, with whole number answers or

with remainders

Find all factor pairs of a number and begin to find common factors of two numbers

Recognise and use simple cube numbers and the notation for cubed (³) such as 2³ =2 x 2 x 2 = 8

Understand and use the vocabulary of prime numbers and begin to use the vocabulary of prime factors and composite (non-prime) numbers

Recall all prime numbers up 19; begin to establish whether a number up to 100 is prime using knowledge of factors

Multiply and divide numbers mentally drawing on known facts, understanding of place value and using a range of strategies

Multiply and divide whole numbers and those involving decimals (with up to three decimal places) by ten, one hundred and one thousand

Multiply numbers with 2 and 3 digits by a two-digit number using the formal written method of long multiplication

Divide numbers with up to 4 digits by a one-digit number using the formal written method of short division, with whole number answers or with remainders

Express remainders as a fraction

Solve word problems involving multiplication using the methods outlined above

Solve word problems involving division using the methods outlined above

Solve missing number problems using known facts

Reason about multiplication/ division e.g. how would you use this fact, 48 ÷ 6 = 8, to solve 96 ÷ 6 =?

Solve number problems and puzzles that involve the above, including knowledge of factors, multiples and square numbers


Solve word problems, which involve division with remainders, using the methods outlined above; begin to interpret remainders in context

Reason about multiplication/division e.g. how would you use this fact, 56 ÷ 7 = 8, to solve 112 ÷ 7 =?

Solve number problems and puzzles that involve the above, including using knowledge of factors and multiples, squares and cubes


Solve word problems involving division; interpret remainders in context

Reason about multiplication e.g. always true, sometimes

true, never true? Multiplying a number always makes it

bigger. Convince me




Nu

mb

er

–

Frac

tio

ns,

de

cim

als

and

pe

rce

nta

ges

Begin to compare and order fractions whose denominators are all multiples of the same number using diagrams, resources and fraction walls to support

Identify, name and write common equivalent fractions using diagrams such as fraction walls to support

Know that fractions can be greater than one whole when the numerator is greater than the denominator and use the term improper fraction

Confidently add fractions with the same denominator, including where the total is greater than one whole

Confidently subtract fractions with the same denominator, including crossing one whole

Find unit and non-unit fractions of whole number quantities e.g. 1/7 of 56; 3/5 of 40; relate to multiplication and division

Recognise and write decimal equivalents of any number of tenths or hundredths

Read, write, order and compare numbers with one and two decimal places

Confidently round decimals with one decimal place to the nearest whole number

Recognise the per cent symbol (%) and understand that ‘per cent’ means ‘per hundred’

Compare and order fractions whose denominators are all multiples of the same number using diagrams, resources and fraction walls to support

Identify, name and write common equivalent fractions beginning to recognise patterns involving factors and multiples

Recognise simple mixed numbers and improper fractions and begin to convert from one form to the other using diagrams to support

Add fractions with the same denominator and begin to add fractions with denominators that are multiples of the same number, including where the total is greater than one whole

Subtract fractions with the same denominator and begin to subtract fractions with denominators that are multiples of the same number, including crossing one whole

Begin to multiply proper fractions by whole numbers, supported by materials and diagrams e.g. 1/ 5 x 3 = 3/5

Begin to recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents

Begin to read, write, order and compare numbers with three decimal places

Round decimals with two decimal places to the nearest whole number

Begin to calculate percentage of quantities using simple fraction equivalence e.g. use 10% = 1/10, 50% = 1/ 2 to find 10% of 120; 50% of 120

Compare and order fractions whose denominators are all multiples of the same number

Identify, name and write equivalent fractions of a given fraction using knowledge of factors and multiples

Recognise mixed numbers and improper fractions and convert from one form to the other

Add fractions with denominators that are multiples of the same number, including where the total is greater than one whole

Subtract fractions with denominators that are multiples of the same number, including crossing one whole

Multiply proper fractions and simple mixed numbers by whole numbers, supported by materials and diagrams e.g. 1¼ x 3 = 3 ¾

Find unit and non-unit fractions of whole number quantities e.g. 1/6 of 420; 5/6 of 30; relate to multiplication and division

Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents e.g. 125/1000 = 0.125

Read, write, order and compare numbers with up to three decimal places, including sets of numbers with different numbers of decimal places e.g. 5.25 > 5.125

Round decimals with two decimal places to the nearest whole number and to one decimal place

Write percentages as a fraction with the denominator 100 and as a decimal e.g. 50% = 50/100 = 0.5

Calculate percentage of quantities using percentage and fraction equivalents of 1/2, 1/4, 1/10 and other fractions with a denominator of a multiple of 10 e.g. 50% of £240 = £120, 10% of £240 = £24, 25% of £240 = £60

Solve problems and puzzles involving numbers with two decimal places in the context of money and measures

Solve problems using fractions to calculate quantities, including non-unit fractions

Reason about fractions e.g. would you rather have 1/6 of £48 or 2/7 of £35? Why?

Solve problems and puzzles involving numbers with two or three decimal places in the context of money and measures

Begin to solve problems which require knowing simple percentage, fraction and decimal equivalents, such as 10% and 50% e.g. find 10 % of £120; what is 50% of £84?

Reason about fractions e.g. If you put these fractions in order, starting with the smallest, which would come third? 3/4, 3/8, 1/2, 5/8, 1/4. How did you work it out?

Solve problems and puzzles involving numbers with up to three decimal places, including in the context of money and measures

Solve problems using unit and non- unit fractions to calculate quantities with confidence

Reason and solve problems which require knowing percentage, fraction and decimal equivalents, such as 10%, 50%, 25%, 20% e.g. There are 80 children in the playground. 25% of them are girls. How many girls and how many boys are there? How did you work it out?

Me

asu

rem

en

t

Begin to use multiplication, division and place value to convert between different units of metric measure

Convert between different units of time e.g. how many seconds in 10 minutes?

Convert between 12 hr and 24 hr digital time, with confidence

Recognise common imperial units still in use today such as inches, pounds and pints and begin to use approximate equivalences between metric units and common imperial units

Measure and calculate the perimeter of a composite rectilinear figure in centimetres and/or metres

Calculate the area of rectangles and squares, using the formula in words, using standards units and notation

Use multiplication, division and place value to confidently convert between different units of metric measure

Calculate the perimeter of a composite rectilinear figure in centimetres and metres, including examples where the length of some sides is not given

Calculate and compare the area of rectangles, including squares, using standard units and notation

Estimate the area of irregular shapes by counting squares

Understand the term volume and cubic centimetres including the notation cm3

Use all four operations to solve word problems involving measures

Solve problems involving units of measurement, including time e.g. How many days is it until your next birthday? How did you work it out?

Solve problems and reason about area and perimeter e.g. The perimeter of a rectangular field is 48m. One of the sides measures 15m. What is the length of the other sides? How did you work it out?

Use all four operations to solve problems involving measure using decimal notation, including scaling, using the above

Solve problems and reason using measurement e.g. draw a rectangle with an area of 36 cm² and a perimeter of 26 cm. Can you find any other rectangles with the same area?




Ge

om

etr

y

Pro

pe

rtie

s o

f sh

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Know that angles are measured in degrees using a protractor

Measure given angles in degrees using a protractor, to the nearest five degrees

Know that angles at a point on a straight line equal 180˚ and is equivalent to half a turn

Know that regular polygons have equal sides and angles

Draw given angles in degrees using a protractor to the nearest 5 degrees

Identify reflex angles

Calculate missing angles on a straight line

Know that angles at a point and one whole turn total 360 ˚

Know that irregular polygons have different length sides and different sized angles

Know all the properties of rectangles, including that all four angles are right angles, opposite sides are equal and parallel and the diagonals bisect one another

Identify 3-D shapes, including cubes and other cuboids, from 2-D representations

Estimate and compare acute, obtuse and reflex angles

Measure given angles in degrees using a protractor to the nearest degree

Draw given angles using a protractor to the nearest degree

Calculate missing angles at a point

Distinguish between regular and irregular polygons based on reasoning about equal sides and angles

Use conventional markings for parallel lines and right angles

Reason about angles e.g. What is the

angle between the hands of a clock when

it is 4 o’clock? At what other times will the

angle between the hands be the same?

Reason about shapes e.g. Is it always, sometimes or never true that the diagonals of a rectangle meet at right angles?

Use knowledge of the properties of rectangles to solve problems about rectangles and the properties of other quadrilaterals, e.g. given the diagonals of a quadrilateral, draw the sides and identify the shape

Po

siti

on

an

d

Dir

ect

ion

Use a grid and coordinates in the first quadrant to translate polygons, describing the new position using co-ordinates

Use a grid and coordinates in the first quadrant to reflect polygons (in lines that are parallel to the axes), describing the new position using co-ordinates

Identify, describe and represent the position of a polygon following a reflection or translation and know the shape has not changed, using coordinates in the first quadrant

Begin to use the second quadrant and the use of negative numbers to plot points, to draw sides to complete a given polygon, to translate and reflect polygons

Stat

isti

cs

Read and interpret information in tables

Read and interpret information in simple timetables, such as TV times, using 12 hour digital time

Complete, read and interpret information in tables

Read and interpret information in timetables, using 24 hour digital time

Use information presented in line graphs using a range of scales

Complete, read and interpret information in timetables using 12 hour and 24 hour digital time

Use information presented in line graphs using a greater

range of scales

Solve problems involving timetables, using 12 hour digital time

Solve comparison, sum and difference problems using information presented in line graphs, with a range of scales

Solve problems involving timetables, using 24 hour digital time

Solve comparison, sum and difference problems using

information presented in line graphs, using a range of scales,

with confidence

Decide which representations of data are most appropriate

and why



Work systematically; record results in a clear and organised

Reason mathematically by following a line of enquiry; make conjectures

Generalise patterns and relationships; form rules in words and make predictions

Communicate concisely using appropriate mathematical language

Make justifications and draw conclusions




Yr. 6 Emerging Developing Securing Extending

Nu

mb

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–

Co

un

tin

g an

d P

lace

Val

ue

Read and write numbers to at least 1,000,000

Order and compare numbers to at least 1,000,000

Round any number to 1,000,000 and beyond to the nearest 10, 100, 1,000, 10,000 or 100,000

Recognise the place value of each digit in numbers to 1,000,000 and beyond

Count forwards and backwards with positive and negative whole numbers, including through zero and begin to describe the term to term rule

Read and write numbers to at least 5,000,000

Order and compare numbers to at least 5,000,000

Round any number to at least 5,000,000 to the nearest 10, 100, 1,000, 10,000, 100,000 or 1,000,000

Recognise the place value of each digit in numbers to at least 5,000,000

Count forwards and backwards with positive and negative whole numbers, including through zero and describe the term to term rule

Interpret negative numbers in a range of contexts

Read and write numbers to 10,000,000

Order and compare numbers to 10,000,000

Round any number to 10,000,000 to the nearest 10, 100, 1,000, 10,000, 100,000 or 1,000,000

Recognise the place value of each digit in numbers to 10,000,000

Use negative numbers in context and calculate intervals across zero

Read Roman numerals to at least 1,000 (M) and recognise years in Roman numerals e.g. the year of their birth

Read and write numbers to 100,000,000

Order and compare numbers to 100,000,000

Round any number to 100,000,000 to the nearest power of ten

Recognise the place value of each digit in numbers to 100,000,000

Understand negative numbers, including decimals, as positions on a number line

Order, add and subtract integers (positive and negative) in context


Reason about number and place value e.g. put the population of five British cities in order of size, starting with the smallest. Explain how you ordered them


Reason about place value e.g. a number rounded to the nearest 10,000 is 1,450,000. What is the largest/smallest number it could be?

Solve number and practical problems that involve all of the above

Reason about number and place value e.g. True or false? The temperature is -3°. It gets 2 degrees warmer. The new temperature is 5°. How do you know?

Reason and solve number and practical problems that involve place value as above

Solve problems in real life contexts involving the addition and subtraction of positive and negative integers

Nu

mb

er

–

Ad

dit

ion

an

d S

ub

trac

tio

n


Subtract numbers with up to 6 digits, including decimal numbers with up to three decimal places, using the formal written method

Add and subtract numbers mentally using a range of efficient strategies


Subtract numbers with up to 7 digits, including decimal numbers with up to three decimal places, using the formal written method

Add and subtract numbers mentally, including with mixed operations, using a range of efficient strategies

Add numbers with up to 7 digits, including decimal numbers with up to three decimal places using the formal written method, with confidence

Subtract numbers with up to 7 digits, including decimal numbers with up to three decimal places using the formal written method, with confidence

Add and subtract mentally with increasingly large numbers and with decimal numbers, including with mixed operations, using a range of efficient strategies; justify methods chosen

Add and subtract numbers with up to 8 digits, including decimal numbers with up to four decimal places, using the formal written method e.g. 4,736.831 + 294,053.5

Strengthen and extend mental methods of calculation accompanied, where appropriate, by jottings

Solve addition and subtraction two-step and multi-step word problems in context, using the above methods

Solve number problems ,including missing number problems, that involve the above

Solve addition and subtraction multi-step word problems in context, using formal written methods

Solve number problems, including missing number problems, that involve the above

Solve addition and subtraction multi-step word problems in context, deciding which operations and strategies to use and why

Solve number problems, including missing number problems, that involve the above

Solve addition and subtraction multi-step word problems in context, deciding which operations and strategies to use and why

Solve number problems and puzzles, some set in a context and some not, that involve the above

Nu

mb

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Mu

ltip

licat

ion

an

d D

ivis

ion

Find all factor pairs of a number; common factors of two numbers; prime factors; common multiples

Recognise cube numbers and the notation for cubed (³) e.g.10³ = 10 x 10 x 10 = 1,000

Recall prime numbers up to 19 and establish whether a number up to 100 is prime by using knowledge of factors and multiples

Multiply and divide numbers mentally, drawing on known facts and knowledge of place value, using a range of strategies and jottings as appropriate

Multiply and divide whole numbers and those involving decimals (with up to three decimal places) by ten, one hundred and one thousand

Multiply multi- digit numbers up to 4 digits by a two-digit number using the formal written method of long multiplication

Divide numbers up to 4 digits using the formal written method of short division, with whole number answers or with remainders expressed as a fraction

Recognise and use in a range of contexts: o Multiples, common multiples,

factors, common factors, prime factors

o Prime numbers to at least 19 o Square numbers to 144

Perform mental calculations, using a range of strategies, with increasingly large numbers

Multiply multi-digit numbers up to 4 digits, including decimal numbers with up to two decimal places, initially in the context of money and measures, by a two-digit number using the formal written method of long multiplication

Divide numbers up to 4 digits using the formal written method of short division with whole number answers or with remainders expressed as a fraction or decimal( with up to two decimal places)

Begin to divide numbers up to 4 digits by a two-digit whole number using a formal written method of long division, without remainders

Begin to use the order of operations to carry out calculations, including the use of brackets

Recognise and use in a range of contexts: o Multiples, common multiples,

factors, common factors, prime factors

o Prime numbers to at least 19; some prime numbers to 100; composite (non-prime)

o Square numbers to at least 144 o Some cube numbers e.g. 2³, 3³, 4³,

5³, 10³

Calculate mentally, using efficient strategies (such as manipulating expressions using commutative and distributive properties to simplify the calculation), including with mixed operations

Multiply multi-digit numbers up to 4 digits, including decimal numbers with up to two decimal places, by a two-digit number using the formal written method of long multiplication

Divide numbers up to 4 digits by a two-digit whole number using a formal written method of long division, with and without remainders; interpret the remainder as appropriate for the context

Use estimation to check answers to calculations and determine an appropriate degree of accuracy

Know the order of operations, including the use of brackets, to carry out calculations involving all four operations (BODMAS)

Recognise and use, in a range of contexts, highest common factors and lowest common multiples

Recognise and derive all prime numbers to 100

Calculate and begin to recognise some square numbers beyond 144 e.g. 13²

Recognise and use square root notation ( )

Recognise the square roots of perfect squares to 12 x 12

Use index notation, beyond squared and cubed, for small positive integer powers e.g. 2⁴ = 2 x 2 x 2 x 2 = 16

Strengthen and extend mental methods of calculation accompanied, where appropriate, by jottings

Multiply multi-digit numbers up to 5 digits, including decimal numbers with up to three decimal places, by a two-digit or a three-digit number using the formal written method of long multiplication

Divide numbers up to 5 digits, including decimal numbers with one or two places, by a two-digit whole number using a formal written method of long division, with and without remainders; interpret the remainder in context

Make and justify estimates and approximations of calculations

Understand how the commutative, distributive and associative laws and the relationship between operations, including inverse operations, can be used to calculate more efficiently

Know the order of operations, including the use of powers, to carry out calculations involving all four operations (BIDMAS)




Use the above to solve problems and puzzles in a range of contexts

Solve word problems involving short and long multiplication

Solve word problems involving short division; interpret remainders in context by rounding up or down

Solve two-step word problems

using a combination of operations;

use mental methods or formal

written methods

Reason about square and cube

numbers e.g. last year my age was

a square number and next year it

will be a cube number. How old am

I? How did you work it out?


Solve word problems involving long multiplication, including in the context of money and measures

Solve word problems involving short division; interpret remainders in context by rounding up/down or by expressing remainders as fractions or decimals, when appropriate

Use mental methods to solve multi-step

word problems using a combination of

operations

Reason about prime numbers e.g. Prime

numbers are the sum of two

consecutive numbers. True or false?


Solve word problems involving long multiplication, short and long division or a combination of these methods, including in the context of money and measures; interpret the remainder as appropriate for the context

Solve multi-step word problems using a combination of all four operations; use mental methods or formal written methods (as above); decide which operations and methods to use; estimate to check answers

Reason about multiplication/ division

e.g. How would you use this fact,

8 x 9 = 72, to solve the following:

0.8 x 9 =? ; 72 ÷ 0.9 =? 0.8 x 0.9 =?


Solve word problems involving long multiplication, short and long division or a combination of these methods, including in the context of money and measures; interpret the remainder as appropriate for the context

Solve two-step or multi-step word problems using a combination of all four operations; use mental methods or formal written methods (as above); decide and justify which operations and methods to use; estimate to check answers

Reason using the above e.g. Is it always, sometimes or never true that multiples of 7 are 1 more or 1 less than a prime number?

Frac

tio

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(in

clu

din

g d

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mal

s an

d p

erc

en

tage

s)

Compare and order fractions whose denominators are all multiples of the same number, including fractions > 1

Identify, name and write equivalent fractions of a given fraction using knowledge of factors and multiples, with confidence

Recognise mixed numbers and improper fractions and convert from one form to the other, confidently

Add fractions with denominators that are multiples of the same number, including where the total is greater than one whole

Subtract fractions with denominators that are multiples of the same number, including crossing one whole

Multiply proper fractions and mixed numbers by whole numbers ¼ x 3 = ¾

Identify the place value of each digit in numbers with up to three decimal places

Read and write decimal numbers as fractions, for example 0.75 as 75/100 and 0.005 as 5/1000

Round decimals with two decimal places to the nearest whole number and to one decimal place, confidently

Read, write, order and compare numbers with up to three decimal places, including sets of numbers with different numbers of decimal places, confidently

Write percentages as a fraction with the denominator 100 and as a decimal e.g. 25% = 25/100 = 1/ 4= 0.25 NB See ‘ratio and proportion’ for calculations involving percentages

Compare and order fractions whose denominators are not always multiples of the same number e.g. which is greater, 2/5 or 1/3

Use common factors to simplify fractions e.g. 4/6 = 2/3

Begin to use common multiples to express fractions in the same denomination e.g. 1/3 and 1/4 can be expressed as 4/12 and 3/12

Add fractions with denominators that are multiples of the same number (using the concept of equivalent fractions) and begin to add mixed numbers

Subtract fractions with denominators that are multiples of the same number (using the concept of equivalent fractions) and begin to subtract mixed numbers

Multiply simple pairs of unit fractions e.g. ½ x ¼ = 1/8

Begin to divide simple proper fractions by whole numbers e.g. ½ ÷ 2 = ¼ (supported by materials and diagrams)

Recall decimal and percentage equivalents of simple fractions e.g. 1/2, 1/4, 3/4, 1/10 (2/10, 3/10 …), 1/5 and express them as equivalent quantities

Calculate using decimals e.g. 0.7 x 60

NB See ‘ratio and proportion’ for calculations involving percentages

Compare and order fractions, including mixed numbers and improper fractions e.g. which is greater 4/5 or 2/3? 2 ½ or 9/4?

Use common multiples to express fractions in the same denomination e.g. 2/3 and 3/5 can be expressed as 10/15 and 9/15

Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions and common multiples

Multiply simple pairs of fractions, writing the answer in its simplest form e.g. 2/3 x 1/2 = 2/6 = 1/3

Divide simple proper fractions by whole numbers

e.g. 1/3 ÷ 2 = 1/6

Associate a fraction with division to calculate decimal/fraction

equivalence e.g. ¾ =3 ÷ 4 = 0.75

Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts NB See ‘ratio and proportion’ for calculations involving percentages

Multiply pairs of fractions, writing the answer in its simplest form e.g. 2/3 x 3/4 = 6/12 = 1/2

Divide non-unit fractions by whole numbers e.g. 3/4 ÷ 2 = 6/8 ÷ 2 = 3/8

Divide simple pairs of proper fractions, writing the answer in its simplest form e.g. 1/3 ÷ 1/2 = 1/3 x 2 = 2/3

Use the equivalence of fractions, decimals and percentages to compare proportions

NB See ‘ratio and proportion’ for calculations involving percentages

Solve problems, including word problems, using the above

Solve problems finding fractions (unit and non-unit) of quantities, including money e.g. 1/7 of £280, 2/3 of 150

Reason about fractions e.g. which is greater, 3/ 4 or 5/8? 3/2 or 5/4? How do you know?


Solve problems finding fractions (unit and non-unit) of quantities, including money and measures e.g. 1/9 of 450km, 5/6 of £120, 7/9 of 108g

Reason about fractions, decimals and percentages e.g. put these in order, starting with the largest: 25%, 0.3, 3/5, 2/10, 0.26. How did you work it out?


Solve problems involving decimals (up to three decimal places) which require answers to be rounded to specified degrees of accuracy

Reason about fractions, decimals and percentages e.g. True or false? 25% of £180 > 4/10 of £160 How do you know?

Solve a wide range of problems involving fractions and decimals

Reason about decimals, percentages and fractions e.g. which would you rather have: 7/8 of £ 640, 0.85 of £650 or 95% of £630? Why? How did you compare these amounts of money




Rat

io a

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(in

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Calculate percentage of quantities e.g. 10% of £360 = £36, 50% of £360 = £180, 25% of £360 = £90 (link to fraction equivalents)

Use a scale factor of two to enlarge a simple shape

Understand ratio as a comparison of part to part and describe ratio using words

Calculate percentage of quantities e.g.20% of £360; 15% of 360 (Find 10% and 5% to calculate 15%)

Use a scale factor of three to enlarge a simple shape

Begin to use notation e.g. 1:3, to describe ratio

Begin to understand proportion as a way to express relationships using fractions

Calculate percentage of quantities e.g. 75% of 360, and use percentages for comparison

Use scale factor (of two or three) to enlarge shapes and find the scale factor of similar shapes

Use notation to describe ratio of two quantities

Understand proportion as a way to express relationships using fractions

Calculate a wide range of percentages of quantities e.g. 16% of £800

Solve problems involving the calculation of percentages in contexts such as 20% of £360

Solve simple problems involving similar shapes where the scale factor is known

Begin to solve simple ratio problems e.g. For every red bulb I plant, I plant 4 white bulbs. If I plant 12 red bulbs, how many white bulbs do I plant?

Solve problems involving the calculation of percentages in contexts such as 15% of £360

Solve problems involving similar shapes where the scale factor is known

Solve simple ratio problems e.g. For every three boys in the playground there are four girls. If there are 15 boys, how many girls are there?

Solve problems involving the calculation of percentages and use percentages for comparison

Solve problems involving similar shapes where the scale factor is known or can be found can be found

Solve ratio problems involving the relative size of two quantities using integer multiplication and division e.g. adapt a recipe for more or fewer people

Solve proportion problems involving unequal sharing and grouping using knowledge of fractions and multiples

Reason about percentages e.g. True or false? 90% of 180g < 80% of 190g. How did you work it out?

Solve problems by calculating percentages and find the outcome of a given percentage increase or decrease

Solve more challenging ratio and proportion problems

Alg

eb

ra

Begin to use symbols and letters to represent variables and unknown numbers and quantities

Begin to express simple missing number problems algebraically e.g. a + 58 = 100

Begin to enumerate possibilities of combinations of two variables e.g. a + b = 100

Describe a simple linear number sequence in words

Use symbols and letters to represent variables and unknown numbers and quantities

Express simple missing number problems algebraically e.g. 6n = 42

Enumerate possibilities of combinations of two variables e.g. n x m = 24

Describe a linear number sequence in words and algebraically

Use symbols and letters to represent variables and unknown numbers and quantities, with confidence

Express more complex missing number problems algebraically by finding pairs of numbers that satisfy an equation with two unknowns e.g. a x 12 = 30 + b

Enumerate all possibilities of combinations of two variables e.g. m x n = 60

Generate and describe a linear number sequence in words and algebraically

Use trial and improvement methods when solving equations

e.g. x³ + x = 20

Expand brackets by multiplying each term inside the bracket by the term outside the bracket

e.g 2(m + 1) = 2m + 2

Find and describe the rule for the nth term of a sequence where the rule is linear

Begin to use symbols and letters in a range of mathematical situations e.g. express the formula for finding perimeter in words and then by using symbols (algebraically)

Begin to describe simple rules algebraically when solving problems

Use symbols and letters in a range of mathematical situations e.g. calculate missing angles expressed algebraically, formula for finding area

Describe simple rules algebraically when solving problems

Use symbols and letters in a range of mathematical situations, with confidence

Describe rules algebraically when solving a range of problems

Describe more complex rules algebraically when solving a range of problems

Me

asu

rem

en

t

Understand use approximate equivalences between metric units and common imperial units, such as inches, pounds, pints, miles

Calculate and compare the area of rectangles, including squares, using standard units and notation; use the formula for area (in words)

Begin to find the area of triangles by dissecting a rectangle

Estimate the area of irregular shapes by counting squares and half squares

Calculate the perimeter of rectilinear shapes and composite rectilinear figures in centimetres and metres, including where the length of some sides is not given

Begin to find the volume of cubes and cuboids (simple examples); use standard units of cm³ and m³

Use, read, write and convert between standard units of metric measures (with up to three decimal places)

Use, read, write and convert between units of time, including 12hour to 24 hour (and vice versa)

Begin to convert between kilometres and miles, knowing that 1km = 5/8 mile

Use the formula (in symbols) for finding the area of rectangles, including squares

Find the area of triangles by dissecting a rectangle

Begin to find the area of parallelograms by dissecting a rectangle

Estimate the area of irregular shapes by counting squares, half squares and fractions of a square

Calculate the perimeter of rectilinear

shapes and composite rectilinear

figures in centimetres and metres,

including where the length of some

sides is not given; express the missing

numbers algebraically

Find the volume of cubes and cuboids, using the formula (in words or symbols); use standard units of cm³ and m³

Convert between kilometres and miles

Recognise that shapes with the same area can have different perimeters and vice versa

Find the area of triangles, understanding and using the formulae (in words and symbols)

Find the area of parallelograms, understanding and using the formulae (in words and symbols)

Calculate, estimate and compare volumes of cubes and cuboids using standard units of cm³ and m³; use other units e.g. mm³, km³; use the formula for finding volume (using symbols)

Use, read, write and convert between all standard units of metric measures (with up to three decimal places) and between all units of time, with confidence

Calculate the area of compound shapes

Find the area of trapeziums, understanding and using the formula (in words and symbols)

Find the circumference of a circle, using practical resources

Find the circumference of a circle, using the formula C = πd (where π = 22/7 or 3.142)




Solve problems involving converting between units of metric measure and units of time

Calculate with time e.g. calculate the length of a train journey given start and end times

Solve measure problems using simple scaling

Reason about measures e.g. When you double the area of a rectangle you double the perimeter. Always true, sometimes true or never true?

Use all four operations to solve problems (including word problems) involving measure, including conversion of units and using decimal notation where appropriate

Solve simple measure problems using scale factor

Reason about measures e.g. A film lasting 140 minutes ends at 18:25. At what time did it start? How did you work it out?

Use all four operations to solve multi-step problems involving all aspects of measure

Solve measure problems using scale factor

Always, sometimes, never true? The area of a triangle is half the area of the rectangle that encloses it.

Reason and solve problems involving all aspect of measurement

Ge

om

etr

y Pro

pe

rtie

s o

f sh

ape

Begin to Illustrate and name parts of a circle, including radius, diameter and circumference

Draw simple 2-D shapes using given dimensions and angles, including the use of a protractor

Begin to recognise conventional markings for parallel lines and angles

Recognise and make nets of a cube

Use angle sum facts to make deductions about missing angles (angles in one whole turn; angles on a straight line)

Know that angles in a triangle total 180°

Illustrate and name parts of a circle, including radius, diameter and circumference

Draw a range of 2-D shapes using given dimensions and angles, including the use of a protractor

Recognise and begin to use conventional markings for parallel lines and angles

Recognise and make nets of simple polyhedron

Know that angles in any quadrilateral total 360°

Find a missing angle in a triangle and any quadrilateral; begin to express a missing angle algebraically

Know that vertically opposite angles are equal

Illustrate and name parts of a circle, including radius, diameter and circumference; know that the diameter is twice the radius

Draw a range of 2-D shapes using given dimensions and angles with increasing accuracy

Identify, compare and classify a wide range of geometric shapes (2-D and 3-D) based on their properties and sizes

Use conventional markings for parallel lines and angles

Recognise and make nets of a range of polyhedron

Find missing angles in a triangle and any quadrilateral; express missing angles algebraically

Calculate missing angles that are vertically opposite; express missing angles algebraically

Identify alternate angles and corresponding angles

Find missing angles around parallel and intersecting lines

Find and calculate the interior and exterior angles of regular polygons

Use conventional markings for equal lines

Solve problems and reason about shapes and their properties e.g. investigate the different nets that would make a cube

Solve problems and reason about shapes and their properties e.g. investigate the different nets that would make given 2-D representations of simple 3-D shapes

Solve problems and reason about shapes and their properties

Reason mathematically to find missing angles

Solve problems using properties of angles, of parallel and intersecting lines and of polygons

Po

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d D

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Identify and describe positions in the first and second quadrant using coordinates (including negative numbers to describe points)

Draw and translate shapes in the first two quadrants and reflect them in y axis

Identify and describe positions beginning to use the full coordinate grid (all four quadrants)

Draw and translate shapes on the coordinate plane (beginning to use all four quadrants) and reflect them in the axes

Identify and describe positions on the full coordinate grid (all four quadrants)

Draw and translate shapes on the coordinate plane (all four quadrants) and reflect them in the axes

Understand and use the language associated with reflections, translations, rotations and enlargement

Transform 2-D shapes by reflection, translation, rotation and enlargement

Solve problems involving coordinates in the first and second quadrants

Solve problems involving coordinates as above

Solve problems involving coordinates in all four quadrants

Solve problems involving reflections, translations, rotations and enlargement

Stat

isti

cs

Interpret a line graph using a range

of scales

Begin to calculate the mean of a

simple set of data

Construct and interpret line graphs using a range of scales

Interpret simple pie charts

Calculate the mean of a simple set of data

Construct and interpret line graphs

using a greater range of scales

Interpret pie charts

Construct simple pie charts

Calculate and interpret the mean as

an average in different contexts

Interpret, construct and compare pie

charts

Calculate range, median and mode of a

set of data and recognise that median and

mode are alternative ways to calculate

averages

Use the above to solve problems in

a range of contexts

Use the above to solve problems in a range of contexts

Use the above to solve problems in a

range of contexts

Decide which representation of data

is most appropriate, drawing on

objectives from previous years and

through cross-curricular work

Solve problems using range, mean,

median and mode

Solve problems involving comparison of

pie charts



Work systematically; record results in a clear and organised way

Reason mathematically by following a line of enquiry and by making conjectures

Identify more complex patterns; generalise and make predictions

Communicate concisely using appropriate mathematical language

Make justifications, draw conclusions and develop mathematical proof


star maths assessment indicators

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